# Help with a special function

• A
Fred Wright
While studying the solution to a integral problem I found online I ran across a special function I am unfamiliar with. The integral is
$$\int_0^{\infty}\frac{t^{\frac{m+1}{n}-1}}{1+t}dt=\mathcal{B}(\frac{m+1}{n},1-\frac{m+1}{n})$$
This certainly isn't the normal beta function. What is it? Can anyone direct me to a reference on this function?

benorin and Delta2

$$\int_0^1 t^{p-1}(1-t)^{q-1}\,dt = \int_0^\infty \frac{z^{p-1}}{(z + 1)^{p+q}}\,dz$$ where $z = t/(1-t)$.